What Are Equivalent Fractions? A Kid-Friendly Guide

Jan 24, 2025 | Allen
Image of shapes

Imagine you have a pizza sliced into 8 equal pieces, and you’re sharing it with 4 friends. Each person gets 2 slices, right? We can figure this out by dividing the total slices by the number of friends: 8 ÷ 4 = 2.

Using fractions, we can say each person’s share is \( \Large \frac{2}{8}\). But guess what? \( \Large \frac{2}{8}\) is the same as \( \Large \frac{1}{4}\)! 

Even though the numbers look different, they represent the exact same amount of pizza. That’s what we call equivalent fractions!

By the end of this guide, you’ll understand how equivalent fractions work and why they’re so useful. Let’s dive in!


What Are Equivalent Fractions?

Equivalent fractions are fractions that represent the same part of a whole, even though they have different numerators (top numbers) and denominators (bottom numbers). This means that the value of the fractions is the same, even if the numbers look different.

Let’s return to our pizza example.

To get evenly sized slices, you probably started to cut your pizza into 4 big parts.

Circle divided into four parts to depict 1/4.

Then you probably sliced it diagonally, halving each of the four slices to get a total of 8:

circle divided into eight parts to depict 2/8.

When you compare the quarter slices (\( \Large \frac{1}{4}\)) with the 2 eighths slices (\( \Large \frac{2}{8}\)), notice how they are equal in size?

Illustration of two equivalent fractions depicted in circles.

That is why we say that fractions like \( \Large \frac{1}{4}\) and \( \Large \frac{2}{8}\) are equivalent.


How to Find Equivalent Fractions

To find out if fractions are equivalent, all we have to do is either multiply or divide both the numerator and denominator by the same number.


Multiplication

To use the multiplication method, simply multiply both the numerator (the top number) and the denominator (the bottom number) of a fraction by the same number. 

Multiplying the numerator and denominator by the same number keeps the fraction’s value the same, even though our numbers will change.

Let’s see it in action using the fraction \( \Large \frac{2}{3}\)

To keep things simple, we’ll multiply it by a small number – number 2.

\( \Large \frac{2×2}{3×2}\) = \( \Large \frac{4}{6}\)

Conclusion: \( \Large \frac{2}{3}\) and \( \Large \frac{4}{6}\) are equivalent numbers.

We can even check this by dividing 2 ÷ 3 and 4 ÷ 6 to compare the results.

2 ÷ 3 = 0.66

4 ÷ 6 = 0.66 


Division

Finding equivalent fractions using the division method involves dividing both the numerator and the denominator of a fraction by the same number. 

This works only if the numerator and denominator share a common factor which is a number that divides both evenly. 

By dividing, we simplify the fraction into a smaller, equivalent form that represents the same value.

Let’s try this with \( \Large \frac{8}{12}\).

To find a common factor, we look for a number that divides both 8 and 12 evenly, such as the numbers 2 and 4. Their greatest common factor (GCF) is 4, so let’s start with that one.

We’ll then divide the numerator and denominator by the GCF:

\( \Large \frac{8 ÷ 4}{12 ÷ 4}\) = \( \Large \frac{2}{3}\)

So, \( \Large \frac{8}{12}\) is equivalent to \( \Large \frac{2}{3}\).

Illustration of two equivalent fractions.

Now, let’s try the other common factor of 8 and 12 which is 2.

\( \Large \frac{8 ÷ 2}{12 ÷ 2}\) = \( \Large \frac{4}{6}\)

So, \( \Large \frac{8}{12}\) is also equivalent to \( \Large \frac{4}{6}\).

How about \( \Large \frac{2}{3}\) and \( \Large \frac{4}{6}\)?

You guessed it! \( \Large \frac{2}{3}\) and \( \Large \frac{4}{6}\) are also equivalent fractions as \( \Large \frac{4}{6}\) can be further simplified into \( \Large \frac{2}{3}\).

Brush up on how to find the greatest common factor:


How Do We Use Equivalent Fractions in Daily Life?

Understanding equivalent fractions isn’t just about doing well in math class—it’s a skill you’ll use in many real-world situations!


Sharing

Let’s return to the first example we talked about. You might notice that \( \Large \frac{1}{4}\) of the pizza for each person is the same as \( \Large \frac{2}{8}\), especially if the pizza is already cut into 8 slices. 

Using equivalent fractions ensures everyone gets their fair share—no arguments needed!


Baking

Most recipes come with specific measurements. To add ingredients properly, you might need to use equivalent fractions. 

For example, you need \( \Large \frac{1}{2}\) cup of sugar for your cake, but your measuring cup only has a \( \Large \frac{2}{4}\) mark. 

When you know that they are the same thing, you will not need to worry about messing up a recipe.


At the Store

While shopping, you might see two packs of juice boxes. One pack says it costs $6 for 12 boxes, and another is $3 for 6 boxes. 

Are these deals the same? 

Using equivalent fractions, you can see that $6/12 simplifies to $3/6, so both packs cost the same per box. This math trick can help you save money!

Illustration of a discounted shelf at the store.


Quiz: Practice Equivalent Fractions

1. True or False:

\( \Large \frac{1}{2}\) is the same as \( \Large \frac{2}{4}\)?


2. Which Fraction is Equivalent to 3/6?

  1. \( \Large \frac{1}{4}\)
  2. \( \Large \frac{1}{2}\)
  3. \( \Large \frac{3}{4}\)


3. Fill in the blank

If \( \Large \frac{4}{8}\) = \( \Large \frac{1}{x}\), what is x?


4. True of False:

Sam says that \( \Large \frac{5}{10}\) is an equivalent fraction of \( \Large \frac{1}{2}\). Is he correct?


FAQs about Equivalent Fractions


1. When Do Students Learn About Equivalent Fractions?

Although fractions are introduced in grades 1-2, they are formally taught in the 3rd grade. 

Equivalent fractions are a foundational concept that helps students understand more advanced math topics. They provide a way to see relationships between numbers and simplify calculations, making them essential in many areas of math.


2. Why Do We Need Equivalent Fractions?

Equivalent fractions help us compare, simplify, and perform operations like addition and subtraction with fractions. They’re a foundational concept in understanding how fractions work and are useful in real-life scenarios, like dividing pizza slices or measuring ingredients in a recipe.

By practicing equivalent fractions, third graders can build a strong understanding of how fractions relate to each other and gain confidence in working with them.


3. What Other Topics or Areas of Math use Equivalent Fractions?

  • Addition and Subtraction: When adding or subtracting fractions, the denominators must be the same. If the fractions have different denominators, you use equivalent fractions to rewrite them with a common denominator. For example, to add \( \Large \frac{1}{2}\) and \( \Large \frac{1}{3}\), you rewrite them as \( \Large \frac{3}{6}\) and \( \Large \frac{2}{6}\) so you can add them easily.
  • Geometry: In geometry, equivalent fractions are used to calculate scale factors and proportions. For example, when working with similar shapes, the ratios of corresponding side lengths are written as equivalent fractions to confirm similarity or find missing dimensions.
  • Decimals and Percentages: Equivalent fractions help you convert between fractions, decimals, and percentages. For instance, knowing that \( \Large \frac{1}{4}\) is equivalent to \( \Large \frac{25}{100}\) makes it easy to write it as 0.25 or 25%. This skill is crucial for real-world applications like budgeting and data interpretation.
  • Algebra: In algebra, equivalent fractions are used when solving equations with rational expressions. For example, simplifying expressions like \( \Large \frac{x}{2}\) = \( \Large \frac{3}{6}\) involves recognizing that \( \Large \frac{3}{6}\) simplifies to \( \Large \frac{1}{2}\), which makes solving for x easier.


Master Equivalent Fractions with Mathnasium of Allen

Mathnasium of Allen’s specially trained math tutors work with elementary school students of all skill levels to help them understand and excel in any math class and topic, including equivalent fractions.

Explore our approach to elementary school tutoring:

At Mathnasium, we assess each student’s current skills and consider their unique academic goals to create personalized learning plans that will put them on the best path towards math mastery.

Whether you are looking to catch up, keep up, or get ahead in your math class, find a Mathnasium Learning Center near you, schedule an assessment, and enroll today!

Schedule a free assessment today with Mathnasium of Allen, TX! 


Psst! Check Your Quiz Answers

  1. True 
  2. B
  3. 2
  4. Yes